Question

Proving $f_n \rightrightarrows f$, provided that $f_n \rightarrow f$, each $f_n$ is increasing, and $f$ is continuous.

score 166 · Answer 1 · 2026-04-17 02:47:57

166

Views

Proving $f_n \rightrightarrows f$, provided that $f_n \rightarrow f$, each $f_n$ is increasing, and $f$ is continuous.

Published on 17 Apr 2026 - 2:47

score 153 · Answer 2 · 2026-04-16 03:44:10

153

Views

Uniform convergence via Arzela-Ascoli

Published on 16 Apr 2026 - 3:44

score 57 · Answer 3 · 2026-04-14 20:33:03

57

Views

Uniform convergence under matrix inverse

Published on 14 Apr 2026 - 20:33

score 130 · Answer 4 · 2026-04-15 03:47:36

130

Views

Rudin: Prove that if $f(x)=\sum_{n=0}^{\infty}c_nx^n$ converges for $|x|<R$, then $f'(x)=\sum_{n=1}^{\infty}nc_nx^{n-1}$ in $(-R, R)$.

Published on 15 Apr 2026 - 3:47

score 60 · Answer 5 · 2026-04-11 17:36:21

60

Views

An attempt at proving Dini's theorem.

Published on 11 Apr 2026 - 17:36

score 35 · Answer 6 · 2026-04-14 13:39:55

35

Views

Uniform continuity of sequence of function

Published on 14 Apr 2026 - 13:39

score 51 · Answer 7 · 2026-04-16 22:06:22

51

Views

Uniform convergence of $f_n(x) = \frac{x^n}{1+x^n}$

Published on 16 Apr 2026 - 22:06

score 168 · Answer 8 · 2026-04-15 13:13:35

168

Views

Sequence of holomorphic functions converges uniformly, but sequence of $k^{th}$ derivatives doesn't

Published on 15 Apr 2026 - 13:13

score 82 · Answer 9 · 2026-04-13 15:59:25

82

Views

Uniform convergence integration question

Published on 13 Apr 2026 - 15:59

score 128 · Answer 10 · 2026-04-15 14:48:30

128

Views

Bounded increments of a martingale converges proof.

Published on 15 Apr 2026 - 14:48

score 37 · Answer 11 · 2026-04-15 22:22:53

37

Views

Find a function $f:[0,1] \to \Bbb R$ such that $f_n \to f$ on $[0,1]$ where $f_n(x)=\sum_{k=0}^n (-1)^k \frac{x^{2k}}{(2k)!}$.

Published on 15 Apr 2026 - 22:22

score 93 · Answer 12 · 2026-04-15 21:38:54

93

Views

Show that $\left(V_{n}\right)_{n \geq 1}$ converges in $L_{1}$

Published on 15 Apr 2026 - 21:38

score 35 · Answer 13 · 2026-04-15 13:37:05

35

Views

$\int_E fd\mu=\lim \limits_{n\to\infty}\int_E f_nd\mu$

Published on 15 Apr 2026 - 13:37

score 150 · Answer 14 · 2026-04-14 15:44:06

150

Views

Rudin’s PMA, Theorem 11.20

Published on 14 Apr 2026 - 15:44

score 75 · Answer 15 · 2026-04-11 19:08:50

75

Views

Does this sequence converge uniformly?

Published on 11 Apr 2026 - 19:08

List Question

Proving $f_n \rightrightarrows f$, provided that $f_n \rightarrow f$, each $f_n$ is increasing, and $f$ is continuous.

Uniform convergence via Arzela-Ascoli

Uniform convergence under matrix inverse

Rudin: Prove that if $f(x)=\sum_{n=0}^{\infty}c_nx^n$ converges for $|x|<R$, then $f'(x)=\sum_{n=1}^{\infty}nc_nx^{n-1}$ in $(-R, R)$.

An attempt at proving Dini's theorem.

Uniform continuity of sequence of function

Uniform convergence of $f_n(x) = \frac{x^n}{1+x^n}$

Sequence of holomorphic functions converges uniformly, but sequence of $k^{th}$ derivatives doesn't

Uniform convergence integration question

Bounded increments of a martingale converges proof.

Find a function $f:[0,1] \to \Bbb R$ such that $f_n \to f$ on $[0,1]$ where $f_n(x)=\sum_{k=0}^n (-1)^k \frac{x^{2k}}{(2k)!}$.

Show that $\left(V_{n}\right)_{n \geq 1}$ converges in $L_{1}$

$\int_E fd\mu=\lim \limits_{n\to\infty}\int_E f_nd\mu$

Rudin’s PMA, Theorem 11.20

Does this sequence converge uniformly?

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